Dual Attitude Representations and Kinematics for Six-Degree-of-Freedom Spacecraft Dynamics

This paper focuses on the development of three newly formed representations of dual attitude and their respective kinematics equations - Dual Classical Rodrigues Parameters, Dual Modified Rodrigues Parameters, Dual Principal Axis and Principal Angle (Dual Principal Rotation Vector). These three formulations are developed by building off of the theories and concepts used with Dual Quaternions and utilizing numerous attitude identities for quaternions to create new identities using dual quaternions and dual attitudes while detailing the process used throughout the derivation. The accompanying dual kinematic equations using these dual attitude parameters are also generated using their respective dual attitude coordinate systems. Furthermore, the new dual attitude representations with their respective, distinct kinematic equations and identities are validated against a simulated 6-DOF rigid body spacecraft control problem to verify equivalency across equations using the dual quaternion as a baseline.